Published on Web 08/16/2008
Transition-Metal Nanocluster Size vs Formation Time and the Catalytically Effective Nucleus Number: A Mechanism-Based Treatment Murielle A. Watzky, Eric E. Finney, and Richard G. Finke* Department of Chemistry, Colorado State UniVersity, Fort Collins, Colorado 80523 Received March 11, 2008; E-mail:
[email protected] Abstract: A mechanism-based equation for the size of a forming transition-metal nanocluster vs time has been derived based on the Finke-Watzky two-step mechanism for transition-metal nanocluster nucleation (A f B, rate constant k1) and autocatalytic growth (A + B f 2B, rate constant k2), where A is the nanocluster precursor and B is the growing nanocluster. The resultant equation expresses nanocluster diameter as a function of time, Dt, in terms of k1, k2, the initial concentration of the nanocluster precursor complex, [A]0, and the number of catalytically effective nuclei derived from either (i) the final nanocluster size, Df, or (ii) the number of atoms in the average catalytically effective nucleus, N*, and the induction period time, tind (N* being by definition the number of atoms present in the average size nucleus at the end of the induction period and when observable catalysis begins). By fitting experimentally determined nanocluster size vs time data using this equation, evidence for the validity of the equation is obtained for Ir0 nanoclusters formed from the well-studied system of H2 reduction of the precursor [(1,5-COD)Ir · P2W15Nb3O62]8-. The Dt equation is then used to determine N* for nine prior Ir0 nanocluster preparations from five different [(1,5-COD)Ir+]n[anionn-] precursors. Also given is a relationship allowing one to interconvert between nanocluster size data and nanocluster precursor concentration data, again when the two-step nucleation and growth mechanism has been shown to apply. Some of the key experimental factors that are known to affect the kinetics of nanocluster formation, and therefore nanocluster size, are also summarized. A look ahead to needed future work is also provided.
Introduction
One of the major goals of nanocluster sciencesthe control over nanocluster sizesis important since, at the nanoscale, cluster properties are highly sensitive to size. The properties that are most often studied as useful applications of nanoclusters include electronics,1 magnetics,2 optics,3 and catalysis.4 Having control over these properties by controlling nanocluster size5 has, therefore, become a “Holy Grail” of the field along with control over nanocluster shape as well as composition.6 Nanoclusters of predetermined size have been prepared by a variety of mostly physical template (e.g., micelle or other template) methods7 as well as seeding methods.8,9 Prior studies attempting to relate nanocluster formation kinetics to size do exist.10,11 However, in a 2004 study only nanocluster growth is treated kineticallysthat is, the crucial nucleation step is ignoredsand a likely incorrect linear diffusional growth is (1) Van Buren, T.; Dinh, L. N.; Chase, L. L.; Siekhaus, W. J.; Terminello, L. J. Phys. ReV. Lett. 1998, 80, 3803. (2) Nakayama, T.; Yamamoto, T. A.; Choa, Y.-H.; Niihara, K. J. Mater. Sci. 2000, 35, 3857. (3) Magruder, R. H., III; Haglund, R. F., Jr.; Yang, L.; Wittig, J. E.; Zuhr, R. A. J. Appl. Phys. 1994, 76, 708. (4) Che, M.; Bennett, C. O. AdV. Catal. 1989, 36, 55. (5) Corain, B.; Schmid, G.; Toshima, N., Eds. Metal Nanoclusters in Catalysis and Materials Sciences: The Issue of Size Control; Elsevier: Amsterdam, 2008. (6) Starkey-Ott, L.; Finke, R. G. Coord. Chem. ReV., 2007, 251, 10751100. One key conclusion of this review is the need for, and current lack of, composition information on transition-metal nanoclusters. 10.1021/ja8017412 CCC: $40.75 2008 American Chemical Society
assumed rather than employing the now well-established step of autocatalytic surface-growth.12 A second interesting 2007 study by Kumar, Gandhi, and Kumar11 looks at Turkevich’s classic AuCl3/citrate3- nanocluster preparation method and the Au0n nanocluster size vs citrate3-/AuCl3 data obtained over 50 years by four different groups (Figure 1 therein11). Unfortunately, this work, too, proceeds from assumed stoichiometries and mechanistic steps, although it does yield a reasonable fit to (7) (a) Prior nanocluster size control typically involves some kind of template to physically limit the growth of the clusters to a particular size. These templates include inverse micelles, resins, gels, and cages.7c–g For example, Pileni has prepared nanoclusters of Au7b and Cu7c in reverse micelles, using H2O concentration to control the size of the clusters (larger clusters were obtained at higher H2O concentration). Microgels7d and resins7e,f have also been used as templates with success, resulting in size-controlled supported nanoclusters. Using a sol-gel method to prepare TiO2 nanoclusters, it was found that lowering the pH of the reaction system led to smaller clusters.7g The use of dendrimers is also common,7h larger nanoclusters being formed in larger, later-generation dendrimers. Pd clusters formed in an apoferritin cage to control their size were found to be active in the hydrogenation of alkenes7i. (b) Petit, C.; Lixon, P.; Pelini, M. P. J. Phys. Chem. 1993, 97, 12974. (c) Lisiecki, I.; Pileni, M. P. J. Am. Chem. Soc. 1993, 115, 3887. (d) Biffis, A.; Orlandi, N.; Corain, B. AdV. Mater. 2003, 15, 1551. (e) Corain, B.; Jerabek, K.; Centomo, P.; Canton, P. Angew. Chem., Int. Ed. 2004, 43, 959. (f) Centomo, P.; Zecca, M.; Corain, B. J. Cluster Sci. 2007, 18, 947. (g) Sugimoto, T.; Xingping, Z. J. Colloid Interface Sci. 2002, 252, 347. (h) D’Ale´ol, A.; Williams, R. M.; Osswald, F.; Edamana, P.; Hahn, U.; van Heyst, J.; Tichelaar, F. D.; Vo¨gtle, F.; De Cola, L. AdV. Funct. Mater. 2004, 14, 1167. (i) Ueno, T.; Suzuki, M.; Goto, T.; Matsumoto, T.; Nagayama, K.; Watanabe, Y. Angew. Chem., Int. Ed. 2004, 43, 2527. J. AM. CHEM. SOC. 2008, 130, 11959–11969
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Watzky et al. Scheme 1
of the critical nucleus size,15–17 nor as we define and use it herein, the catalytically effective nucleus. The main reason for this void is clear: until 1997 there were no detailed kinetic and mechanistic studies of transition-metal nanocluster formation that (a) started with a balanced nanocluster formation reaction, (b) yielded compositionally well-characterized nanoclusters, and which (c) included discrete mechanistic steps and rate constants that are the hallmarks of rigorous mechanistic studies (i.e., rather than just word statements of the “mechanism” which, of course, cannot be used to quantitatively fit kinetic data).12 Figure 1. (a) Established balanced stoichiometry for H2 reduction of the polyoxoanion-supported Ir complex [Bu4N]5Na3[(1,5-COD)Ir · P2W15Nb3O62] in acetone and with cyclohexene present to form, on average, Ir0∼300 nanoclusters for the specific conditions employed (see the Experimental Section). The nanoclusters are then good cyclohexene hydrogenation catalysts so that their formation can be followed indirectly, but in real time, by their hydrogenation activity and the pseudoelementary step method summarized by eqs 1a-d. (b) Observed kinetic curve for cyclohexene loss, and by eq 1d, the desired conversion of A into B. The fit shown is to the two-step, mechanism in Scheme 1 of A f B and A + B f 2B, with resultant k1 ) 0.022(1) h-1 and k2 ) 4.28(6) × 103 M-1 h-1.
the nanocluster size vs citrate3-/AuCl3 data. Perhaps most significantly, those authors use a so-called number- or population-balance approach to estimate the number density (concentration) of particles.11,13 A valuable study by W. Yang, X. Peng, and co-workers examines the effects of the Na3[citrate3-]/ HAuCl4 ratio on the size of Aun nanoclusters made in water at 100 °C in a version of Turkevich’s classic synthesis. They found that it is actually the pH and pH-dependent speciation, [AuCl4x(OH)x] (x ) 0 at pH 3.3 to x ) 3 at pH 8.1), that are the underlying key variables in that complicated system.14 However, to date, no prior study uses a kinetically verified mechanism fortified by a balanced nanocluster formation reaction to formulate equations that can calculate transitionmetal nanocluster size vs their formation time. Nor is there any mechanism-based treatment which deals with the important topic (8) Although nanocluster size control using seed clusters is well established, this method presumes the availability of small seeds of controlled size, narrow size dispersion, and known composition, something that is more rare. Buhro and co-workers have cleverly used Au∼101(PPh3)21Cl5 as seeds for Bi, In, and Sn nanoclusters with excellent results in size-dispersion control.8b Sau et al. used small gold nanoclusters as seeds for larger Au clusters;8c the sizes of the UV irradiation prepared seeds were controlled by the amount of reductant and nanocluster stabilizing ligand. Murphy et al. has examined the effects of rate of monomer addition to seeds on the growth of Au clusters on those seeds.8d Other examples of the seed method are available in the literature (e.g., see the refs summarized in the following references). (b) Yu, H.; Gibbons, P. C.; Kelton, K. F.; Buhro, W. E. J. Am. Chem. Soc. 2001, 123, 9198. (c) Sau, T. K.; Pal, A.; Jana, N. R.; Wang, Z. L.; Pal, T. J. Nanopart. Res. 2001, 3, 257. (d) Jana, N. R.; Gearheart, L.; Murphy, C. J. Chem. Mater. 2001, 13, 2313. (9) Watzky, M. A.; Finke, R. G. Chem. Mater. 1997, 9, 3083. (10) Hiramatsu, H.; Osterloh, F. E. Chem. Mater. 2004, 16, 2509. (11) Kumar, S.; Gandhi, K. S.; Kumar, R. Ind. Eng. Chem. ReV. 2007, 46, 3128. (12) Watzky, M. A.; Finke, R. G. J. Am. Chem. Soc. 1997, 119, 10382. (13) Dixit, N. M.; Zukoski, C. F. Phys. ReV. E 2002, 66, 051602. (14) Ji, X.; Song, X.; Li, J.; Yang, W.; Peng, X. J. Am. Chem. Soc. 2007, 129, 13939. 11960
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The Finke-Watzky Two-Step Mechanism of Transition-Metal Nanocluster Formation. The 1997 Finke-
Watzky (hereafter F-W) two-step mechanism for transitionmetal nanocluster formation from metal salts under reductive conditions, such as H2, is shown in Scheme 1,12 in which A represents a reducible organometallic or inorganic precursor to the final nanoclusters and B represents the growing surface of the (e.g., Ir0) nanocluster (Figure 1a). The rate constants k1 and k2 for nucleation and autocatalytic growth, respectively, are determined via the established pseudoelementary step method using cyclohexene hydrogenation as a fast catalytic reporter reaction, eq 1,18 where the factor of 1200 in eqs 1c and 1d is just the experimentally chosen ratio of cyclohexene to nanocluster precursor, A. The established, balanced reaction stoichiometry and a typical resulting, “S”shaped sigmoidal kinetic curve for the prototype Ir0 nanocluster system are shown in a and b of Figure 1, respectively. The sigmoidal curve consists of a flat, initial induction period during which nucleation is generally believed to occur. It has been experimentally demonstrated elsewhere12 that k1 is inversely proportional to the length of the induction period, i.e., k1 (units: time-1) ∝ 1/tinduction (units: time-1).
The induction period is then followed by fast autocatalytic reduction of the precursor A onto the nanocluster surface B. Also shown elsewhere12 is that k2 at constant [A]0 (and more generally k2 × [A]019) is directly proportional to the normalized slope of the linear part of the curve after the induction period, (15) Volmer, M.; Weber, A. Z. Phys. Chem. (Leipzig) 1926, 119, 227. (16) Volmer, M. Kinetik der Phasenbildung (Kinetics of Phase Formation); Steinfopff: Leipzig, 1939. (17) Becker, R.; Do¨ring, W. Ann. Phys. 1935, 24, 719. (18) Lin, Y.; Finke, R. G. J. Am. Chem. Soc. 1994, 116, 8335. (19) Watzky, M. A; Ott, L. S.; Finney, E. E.; Finke, R. G. TransitionMetal Nanocluster Nucleation Kinetic and Mechanistic Studies, manuscript in preparation.
Transition-Metal Nanocluster Size
that is, k2 × [A]0 (units: time-1) ∝ slope/[A]0 (units: time-1), where [A]0 represents the initial concentration of precursor A. Overall, the mechanism in Scheme 1 is the simplest kinetic model that has proven able to fit a wide body of nanocluster nucleation and growth kinetic data9,12,20 (i.e., an “Ockham’s razor”21 treatment, Ockham’s razor being a basic tenant of rigorous mechanistic science). In more recent work, two additional steps have been discovered that occur following nanocluster formation, the steps of nanocluster bimolecular agglomeration (B + B f C, rate constant k3)22 and autocatalytic agglomeration (B + B f 1.5C, rate constant k4).23–25 Since the self-assembly reaction that we call nanocluster formation necessarily consists of many steps, for example at least 300 (and probably more like 1000 or more) even for the formation of a “simple” Ir∼300 nanocluster as shown back in Figure 1, some simplification and assumptions are necessary to obtain k1 and k2 from the kinetic data such as that shown in Figure 1. These simplifications and underlying assumptions, while already detailed in our prior papers,12,20,24 are briefly summarized in the Supporting Information for the convenience of the interested reader. The assumption most relevant to the treatment of size vs time herein is that k1 and k2 are assumed to be independent of size. That is, aVerage k1 and an aVerage k2 rate constants are obtained from the curve-fits, such as that shown in Figure 1, and are then employed in the nanocluster size vs time equations which follow. With a bit of reflection, one realizes that the size of the nanoclusters will depend on how many nuclei form, when nucleation effectively stops, and when growth begins (i.e., in the case where nucleation and growth are largely separated in time, Vide infra, as desired for nanoclusters with a narrow size dispersion). Noteworthy here is that the induction time (i.e., the k1 ∝ 1/tind) and the fast downturn (i.e., k2 × [A]0 ∝ slope/ [A]0) seen in Figure 1 is generally consistent with a separation in time of nucleation and growth. Further reflection makes it clear that nanocluster size should be related to the rate constants k1 and k2, as well as the initial metal concentration [A]0, that is, when k2[A]0/k1 is large, relatively few nuclei grow quickly into larger nanoclusters, whereas when k2[A]0/k1 is small, more nuclei are being formed that are growing relatively slowly so that smaller nanoclusters are expected. Initial evidence that the k2[A]0/k1 ratio correlates at least somewhat with nanocluster size was published in 1997.9 In what follows, we will therefore also look at the limits of the nanocluster diameter vs time, Dt, equation in the two limits of k2[A]0/k1 .1 and k2[A]0/k1 ,1. The Focus of the Present Contribution: the Dependence of Nanocluster Size on k1, k2, [A]0 and N*, the Number of Atoms in the Catalytically Effective Nucleus. Herein we (i) show
that the F-W two-step mechanism for nanocluster nucleation followed by autocatalytic growth can be used to provide an equation predicting nanocluster size vs time in terms of k1, k2, ¨ zkar, (20) (a) Ott, L. S.; Finke, R. G. Inorg. Chem. 2006, 45, 8382. (b) O ¨ zkar, S.; S.; Finke, R. G. J. Am. Chem. Soc. 2005, 127, 4800. (c) O Finke, R. G. Langmuir 2003, 19, 6247. (d) Widegren, J. A.; Finke, R. G. Inorg. Chem. 2002, 41, 1558. (e) Weddle, K. S.; Aiken, J. D., III; Finke, R. G. J. Am. Chem. Soc. 1998, 120, 5653. (21) Hoffmann, R.; Minkin, V. I.; Carpenter, B. K. Int. J. Philos. Chem. 1997, 3, 3. (22) (a) Hornstein, B. J.; Finke, R. G. Chem. Mater. 2004, 16, 139. (b) See also the addition/correction in: Hornstein, B. J.; Finke, R. G. Chem. Mater. 2004, 16, 3972. (23) Besson, C.; Finney, E. E.; Finke, R. G. J. Am. Chem. Soc. 2005, 127, 8179. (24) Besson, C.; Finney, E. E.; Finke, R. G. Chem. Mater. 2005, 17, 4925. (25) Finney, E. E.; Finke, R. G. Chem. Mater. 2008, 20, 1956.
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and [A]0, and if the final size of the nanoclusters is known by, say, transmission electron microscopy (TEM) or other means. Also discussed is why it is not possible yet to predict the size vs time ab initio and unless either the final size, Df, or the number of nuclei formed are known. However, we also (ii) show that with the assumption of a complete separation of nucleation and growth in time, the nanocluster size (Dt) vs time equation can be expressed in terms of the known k1, k2, [A]0, and the final nanocluster size (Df). We then (iii) obtain and present experimental TEM vs size data and show that this experimental data can be fit by, and thus conforms to, the Dt equation that is derived. We also (iv) use other TEM final size vs time data to calculate the catalytically effective nucleus number, N*, for nine other Ir0 nanocluster nucleation and growth systems previously examined in our laboratories. We furthermore (v) examine the limiting cases of very low and very high [A]0, as well as the resulting k1 . k2[A]0 and k1 , k2[A]0. Finally, we (vi) summarize the known experimental variables that influence k1 and k2, and, therefore, also control nanocluster size, and we (viii) list some needed additional experiments and studies. Overall, this is the first contribution that treats the important and timely topic of nanocluster size control, and the related topic of the number of atoms in the catalytically effective nucleus (and, therefore, that nucleus’ corresponding size) via a kinetically documented nanocluster formation mechanism. Experimental Section General Considerations. All manipulations were carried out under air-free conditions using a Vacuum Atmospheres N2 drybox maintained at e5 ppm O2 as monitored by a Vacuum Atmospheres O2-level monitor. Unless indicated otherwise, all commercially available solvents, compounds and materials were used as received. Acetone (Burdick and Jackson, water content
